Short course Multi-trait
LAPEA

Outline

Background

Phenotypic, genetic and environmental correlation

flowchart LR
  A[Hard edge] --> B(Round edge)
  B --> C{Decision}
  C --> D[Result one]
  C --> E[Result two]

Genetic correlation

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Direct and indirect selection

In direct selection, the selection criteria is based on the trait(s) of interest. For example, if the trait of interest is grain yield in the target environment, selections are made using grain yield data from trials conducted in the target environment.

In indirect selection, the criteria is based on traits that may be associated with grain yield such as biomass yield, grain size, number of inflorescences, etc., would be considered indirect selection, and such traits are called secondary traits. Likewise, selection based on the trait of interest measured in an environment that does not represent the target environment can be considered indirect selection: For instance, if the target environment is tropical, grain yield measured in a temperate environment would be considered a secondary trait and selection based on this trait would be considered indirect selection. Genomic selection is a form of indirect selection because selection is based on a genotype and not directly on phenotypic values. Indirect selection is often used to eliminate a fraction of the selection units prior to selection on the trait of interest especially when the trait of interest is expensive to measure. For example, in rice breeding, the cost of conducting sensory evaluations to assess grain quality is so high, quality can only be measured on relatively few evaluation units. Therefore, to breed for good or acceptable quality, rice breeders measure and select based on traits which are associated quality such as amylose content.While indirect selection can be a useful. It has been often used ineffectively. For example, U.S. maize breeding in the early 1900s relied on selection based on appearance of the ear judged at “corn shows” (Bowman and Crossley, 1908) in attempt to develop better yielding maize varieties. In small grain crops, visual selection for yield component traits was often done to try to improve grain yield. This strategy has since been shown to be an ineffective (McGinnis and Shebeski, 1968; Rasmusson and Cannell, 1970). To determine if indirect selection would be more effective than indirect selection, a metric called the relative efficiency can be computed. The relative efficiency of indirect vs. direct selection is simply the ratio of the expected genetic gain due to indirect selection to the expected gain due to direct selection (Lerner and Cruden, 1947). Assuming the population sizes and number of individuals selected is constant, the relative efficiency of indirect and direct selection depends the selection accuracy of indirect selection as well as the genetic correlation between the indirect and direct selection criteria (Fig. 3). For the case of indirect selection based on markers, indirect selection accuracy equals one, because a marker genotype is completely heritable. In most cases direct selection is more effective than indirect selection. When much larger population sizes are possible with indirect selection compared to direct selection, there is a greater chance that indirect selection would be a more favorable strategy.

Multistage selection

Multistage selection: Selection for different traits at different stages during cultivar development.

Tandem selection

Selection for one trait until that trait is improved, then for a second, etc., until finally each has been improved to the desired level.

Independent culling levels

A certain level of merit (minimun level of performance) is established for each trait, and all individuals below that level are discarded regardless of values for other traits.

Index selection

Select for all traits simultaneously by using some index of net merit.

Another slide 3

\begin{gather*}
a_1=b_1+c_1\\
a_2=b_2+c_2-d_2+e_2
\end{gather*}

\begin{align}
a_{11}& =b_{11}&
  a_{12}& =b_{12}\\
a_{21}& =b_{21}&
  a_{22}& =b_{22}+c_{22}
\end{align}

Uni-trait model

The BLUP methodology uses mixed models for the genetic analysis and provides accurate and least biased prediction of breeding values.

Mixed model formulation

\[ y = Xb + Zu + e \]

Advantages

• It handles missing data

Advantages

Furthermore, it can be extended to incorporate/account for more complicated effects, such as:

• Interaction terms (e.g GXE)

• Covariance and correlation structures (relationship matrices and Correlation matrices)

• Heterogeneous variances

• Correlated traits

Multi-trait model

\[\begin{gather*} y_{i} = X_{i}b_{i} + Z_{i}u_{i} + e_{i} , & i = 1, 2 \end{gather*}\]

\[\begin{align} \begin{bmatrix} y_{1} \\ y_{2} \\ \end{bmatrix} = \begin{bmatrix} X_{1} & 0 \\ 0 & X_{2} \\ \end{bmatrix} \begin{bmatrix} b_{1} \\ b_{2} \\ \end{bmatrix} + \begin{bmatrix} Z_{1} & 0 \\ 0 & Z_{2} \\ \end{bmatrix}\begin{bmatrix} u_{1} \\ u_{2} \\ \end{bmatrix} + \begin{bmatrix} e_{1} \\ e_{2} \\ \end{bmatrix} \end{align}\]

Advantages

Hands-on using R

 Installing packages
 
 # Github version
 install.packages('devtools');
 library(devtools);
 install_github('covaruber/sommer')
 
 # or
 
 # CRAN version
 install.packages('sommer',dependencies = TRUE))
 library(sommer)